Mathematician and physicist J. Willard Gibbs described thermodynamic equilibrium and developed the science of statistical mechanics. His PhD, in 1863, was the first doctorate in Engineering earned in America. He wrote his most famous paper, "On the Equilibrium of Heterogeneous Substances", in 1876, and after it was published James Clerk Maxwell mailed Gibbs a handmade three-dimensional model of the thermodynamic surface Gibbs had described. His classic text, Elementary Principles in Statistical Mathematics, was published in 1902, just months before his death.

He never married, lived alone, never sought membership in any scientific organization, and reportedly eschewed most social contact outside of academic circles. Respected but hardly famous in his own time, Gibbs' work was widely noticed only after his death, and he has since been acknowledged as among the greatest theoretical scientists. His observations on classical physics, described as "abstruse but beautifully logical", are generally applicable in quantum mechanics as well. He also invented and patented a mechanical brake for railroad cars.

His father, Josiah Willard Gibbs, Sr., was a philology professor at Yale, and served as translator and English tutor for Joseph Cinqué and other Africans who seized the slave ship Amistad and sought freedom in America.